Prove that a square cannot be dissected into an odd number of triangles of equal area.

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# A problem that appeared on AMM

# ELMO 2012 SL N9

# ELMO 2012 SL A9

# Continued Fractions and Linear Fractional Transformations

# Putnam 2014 B6

# Putnam 2014 A5

# Romania 2013 p4 grade 12

Prove that a square cannot be dissected into an odd number of triangles of equal area.

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Are there positive integers such that there exist at least positive integers such that both and are perfect squares?

Let be distinct positive real numbers, and let be a positive integer greater than . Show that

and

This is an article written by Evan O’Dorney for Intel STS 2011. It deals with rational approximation to some square roots. The article is at here

Let be a function for which there exists a constant such that for all Suppose also that for each rational number there exist integers and such that Prove that there exist finitely many intervals such that is a linear function on each and

Let Prove that the polynomials and are relatively prime for all positive integers and with

Given a natural number, a body with commutative property that a polynomial of degree and a subgroup of the additive group , Show that there is so .